# A population has a mean μ=83 and a standard deviation σ=2424.Find the mean and standard deviation of a sampling distribution of sample means with sample size n=64.

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A population has a mean μ=83 and a standard deviation σ=2424.
Find the mean and standard deviation of a sampling distribution of sample means with sample size n=64.
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Step 1

Given data

Mean μ=83

Standard Deviation σ=24

Points on sampling distribution of the sample mean:

• If the true population distribution of a random variable, say, x, is normal with parameters, mean μ and standard deviation σ, then, whatever be the size (n) of the sample taken from the population, the distribution of the sample mean is also normal, with parameters, mean μ and standard deviation σ/√n.
• Even if the true population distribution of a random variable, say, x, is not normal and has population mean μ, standard deviation σ, then, for a large size (n ≥ 30) of a sample taken from the population, the distribution of the sample mean is approximately normal, with parameters, mean μ and standard devia...

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